CIRED
22nd International Conference on Electricity Distribution
Stockholm, 10-13 June 2013
Paper 1100
REQUIREMENTS-DRIVEN DISTRIBUTION STATE ESTIMATION
Euan DAVIDSON
Andrew KEANE
Smarter Grid Solutions – UK
University College Dublin – Ireland
edavidson@smartergridsolutions.com
akeane@ucd.ie
Neil MCNEILL
Smarter Grid Solutions – UK
nmcneill@smartergridsoultions.com
David MACLEMAN
SSE Power Distribution - UK
david.macleman@sse.com
ABSTRACT
This paper describes the development of distribution state
estimation for trial on the Orkney Isles in the north of
Scotland. The paper discusses the techniques selected for
the trial based on the requirements of the distribution
network operator. The techniques include the use of a
novel error estimation technique that calculates an error
interval for data derived via distribution state estimation.
INTRODUCTION
The proliferation of distributed energy resources (DER)
and anticipated changes to load patterns are changing the
planning and operation of distribution networks. Issues
associated with the connection of DER, such as
congestion, voltage-rise and voltage-step-change, have
led to the requirement for greater visibility of such
networks. However, the need for visibility has to be
balanced against the cost of additional measurement and
telemetry, including possible redundancy. Distribution
state estimation (DSE) offers the possibility of using a
reduced set of measurements, augmented with pseudomeasurements, to provide extended visibility of
distribution networks. As a result, Scottish and Southern
Energy Power Distribution (SSEPD), the Distribution
Network Operator (DNO), is trialling the use of DSE on
the Orkney Islands in Scotland, an area of network with
significant connection of distributed generation and
additional yet untapped renewable energy resources. This
activity is set in the context of the wider deployment of
an active network management scheme on Orkney, which
has been operational for three years and has enabled an
additional >20 MW to connect to a network previously
considered full [1], representing one of the leading smart
grid deployment projects in Europe. DSE is one of the
further developments being implemented in the next
generation of the active network management scheme on
the Orkney Isles [2].
Robert CURRIE
Smarter Grid Solutions – UK
rcurrie@smartergridsolutions.com
Martin LEE
SSE Power Distribution - UK
martin.lee@sse.com
quantities derived from those estimates, e.g. current and
power flow. This requirement has yet to appear in the
literature on DSE but received consideration in research
into classical state estimation problems.
For the Orkney Island trials, the problem of error
estimation was address by adapting the method originally
presented in [3][4] and augmenting the functionality of
SGS’s existing distribution state estimator, sgs visibility,
to utilize that adapted method. The method exploits the
full measurement Jacobian for a converged state estimate
and the measurement residuals, as produced by sgs
visibility, as well as knowledge of the transducer errors.
This paper discusses the nature of further results and the
validity of the assumptions on which the method is based.
The impact of error estimation on the use of the output of
distribution state estimation, as a tool for supporting
network operation and as a potential input to active
network management, is also discussed.
DISTRIBUTION STATE ESTIMATION
DSE has been the subject of numerous papers [5-13].
DSE problems differ from classical state estimation
problems in that the limited number of measurements
renders most DSE problems mathematically underdetermined.
Whilst [5-13] illustrate several different formulations of
distribution state estimation problems, the DSE
techniques discussed in this paper are based on weighted
least squares (WLS) methods which involved providing
the state estimator with additional pseudo-measurements,
in our case estimates of load, which render the state
estimation problem over-determined and hence tractable
using more traditional state estimation methods. Our
selection of state estimation method has been influenced
by the results reported in [13].
DSE ON ORKNEY
In this paper, we discuss the DNO’s requirements for
distribution state estimation and the techniques which
were selected based on those requirements. During the
requirements elicitation process, a requirement emerged
for an online method for computing the error bounds of
the state variables estimated by the DSE and additional
CIRED2013 Session 4
Paper No 1100
The Orkney Isles, to the north of the Scottish mainland,
are an area of considerable reserves of renewable energy.
The islands rank amongst the windiest places in Europe,
where the capacity factor of wind generation regularly
exceeds 40%. The area also hosts the European Marine
Energy Centre, with significant wave and tidal resource
CIRED
22nd International Conference on Electricity Distribution
Stockholm, 10-13 June 2013
Paper 1100
in the waters around the island. In the mid-2000s the
network on Orkney had reached capacity for connection
of distributed generation. In order to avoid prohibitively
expensive reinforcement of the submarine cable
connections to the mainland, an active network
management scheme was deployed on the island to
manage connected generation under non-firm connection
agreements [1][2].
Constraints on the network are primarily thermal;
however, the increasing level of penetration of distributed
generation is expected to present voltage control
challenges and the relatively observable nature of the
network make it an attractive site for the trials of DSE. It
is an area of network which is planned and operated in an
active manner and, as a result, greater visibility of the
network would be beneficial to the DNO. SSEPD wishes
to trial the use of DSE on Orkney to assess its
performance and potential application for other locations
in its licence areas. It is expected that the deployment of
DSE on an existing active network management platform
will further demonstrate a least cost and efficient means
of deploying smart grid functionality.
The network on Orkney is reasonably well instrumented.
The network model used by the DSE comprises 70 buses
with 76 branches. Voltage at 15 of the busbars is visible
to the control room, as are flows or current on 30 of the
branches. Studies carried out by Smarter Grid Solutions
have shown that DSE, without employing pseudomeasurements, increases the observability index of the
network from 25.86% to 83.56%. The addition of a small
number of pseudo-measurements can increase
observability to 100% at 33 kV and at primary
substations (33/11 kV).
DSE Requirements
Initial trials are to focus on the 33kV network and 11kV
primary substations.
SSEPD has identified the
requirement for:
 Security, capacity, performance, availability,
and configurability;
 The ability to identify areas of the network
where a state estimate can be calculated;
 The identification of bad/erroneous data;
 The ability to provide an estimate of the error in
the resulting state estimate; and
 Timely production of state estimation data;
Most of the requirements above can be met with
techniques available in the literature on DSE. Below we
detail our selected methods and the rationale for their
selection. Error estimation is given special treatment in
that we have selected a technique not normally applied to
distribution networks. We present the results of offline
studies based on historical data to indicate the sort of
performance we expect to see during online DSE trials.
CIRED2013 Session 4
Paper No 1100
DSE Methods
Observability Analysis
Observabililty analysis involves identifying observable
islands, contiguous sets of buses for which, given the
available measurements and pseudo-measurements, a
state estimate can be calculated. sgs visibility uses a
numerical method based on Gaussian elimination, similar
to the method described in [14].
State Estimation
For each observable island a state estimate is calculated.
sgs visibility employs the Hachtel method for state
estimation [15]. In the Hachtel method, virtual
measurements and regular measurements are represented
as equality constraints. This leads to increased numerical
stability of the state estimator as the coefficient matrix is
less likely to be ill-conditioned.
Bad Data Detection
Once a state estimate for an observable island has been
calculated, sgs visibility uses the maximum normalised
residual technique for identifying bad data [15]. Should
bad data be identified, it is removed and the DSE process
is started again with the reduced data set omitting the
offending
measurand/pseudo-measurement.
New
observable islands are identified, state estimates for each
island are calculated and bad data detection repeated.
This process is executed recursively until the DSE has
found a set of state estimates for a set of observable
islands with no bad data.
Error Estimation
SSEPD requires a means of estimating the error of the
output of the state estimator. This is a novel facet of the
DSE being deployed on Orkney. As a result we have
described the approach in the following section.
ERROR ESTIMATION
The error estimation module of sgs visibility uses the
method described in [3][4]. The method determines the
maximum and minimum possible error in individual
estimated states, i.e. bus voltage magnitude and angle,
based on the solved measurement Jacobian, transducer
errors and measurement residuals. A set of optimisations
are solved for each state variable or quantity derived from
state variables that we wish to calculate an upper and
lower bound for, e.g. branch flows.
The objective functions of the method can be expressed
as follows,
: ∀
1
1
: ∀
where dxi is the change in the ith state variable for N state
variables. For a given solved island of N buses the error
bound calculation entails 4N-2 calculations.
CIRED
22nd International Conference on Electricity Distribution
Stockholm, 10-13 June 2013
Paper 1100
+ - estimate, *-upper bound,  - lower bound
Figure 1: Voltage magnitude state variable estimates and calculated error bounds.
the maximisation or minimisation of the ith state.
The problem is formulated as a linear programme, with
2N-1 calculations to determine the minimum possible
bounds and another 2N-1 calculations to determine the
maximum possible bounds. The slack bus has a reference
angle of 0 radians and hence no error bound calculation is
required for the slack bus angle.
For any given measurement, there will be a measurement
error, owing to the calibration and specification of the
transducer employed, given as τ. This is taken account of
by adding and subtracting τ to and from the residual, i.e.
the difference between the measured states and the
estimated states,
∆
τ
where ∆ is the residual associated with the jth
is the calculated (expected)
measurement and
values for the various measurements arising out of a
converged state estimate solution. The resulting vectors
of m values are given as Δzl and Δzu . These values are
the upper and lower bounds of the inequality constraints
in the formulation. In the case of virtual measurements
there is no transducer error, i.e. τ=0. The full
measurement Jacobian contains the sensitivity of each of
the measured quantities, including virtual measurements,
to changes in the estimated state variables. The set of
inequality constraints relating to these quantities can be
expressed as follows,
∆
∆
∆
where
is the full measurement Jacobian obtained
from the converged solution of the state estimator and Δx
is the vector of changes in state determined by the linear
programme, commonly referred to as the control or
decision variable. For each iteration the state being
maximised/minimised (i) is incremented by one, i.e. for
any given solution to the linear programme, it is only the
change in the ith state (dxi) that is of relevance. Values
are calculated for all other states, but these values are
adjusted by the linear programme as necessary to achieve
CIRED2013 Session 4
Paper No 1100
Figure 1 shows a set of results for the largest observable
island on Orkney without using pseudo-measurements.
Implicit in this method is the fact that states in the
network for which there are no or very few associated
measurements of any kind, the error bounds will be
significant and will generally represent an accumulation
of the transducer errors. This can be seen in the outliers in
figure 1, at bus 20, 22, 24, 36, 44, and 54. These buses
are located on remote parts of the network, each one
being four to five buses away from a measurement.
Studies indicate that pseudo-measurements can tighten
these bounds. The sparsity of the
is also of
relevance here. For weakly interconnected systems, it
will tend to be sparse, essentially providing less
restriction on the error bounds. Simply put, each value in
relates a measurement to a state, the less non-zero
entries the less information available on the unmeasured
states, of which typically there are many.
Another point to note is the assumption of linearity
around a given operating point. In [4], two formulations
of the error estimation problem were compared: one
based on a linearised model solved using linear
programming and a non-linear formulation solved with
computationally more intensive quadratic programming.
The results in were comparable; however, it may be
possible that weights and corresponding τ of any pseudomeasurements would challenge the linearity assumption.
Further investigation in this area is required, with
potential for the application of non-linear programming
techniques.
In terms of time to compute a solution, the method set out
in [3][4] requires a significant number of linear
programmes to be solved in order to calculate state
estimates. For a network the size of Orkney, this takes
around 2 seconds on a standard server. However, given
that each linear programme is independent, these could
be solved concurrently on different cores of the server,
reducing the time to compute a solution.
CIRED
22nd International Conference on Electricity Distribution
Stockholm, 10-13 June 2013
Paper 1100
DSE AND ANM
As discussed at the start of the paper, Orkney hosts one of
the leading smart grid deployments in Europe. The ANM
scheme on Orkney has been in operation since 2009.
Whilst the ANM scheme on Orkney does not utilise DSE,
the proposed use of DSE within the context of ANM is
not new: GenAVC [16] exploited DSE to reduce
measurement costs. AuRA-NMS [17], which tackled both
voltage and thermal issues, also proposed the use of DSE
to those ends but no trials were ever undertaken as part of
that project even though several approaches to DSE were
developed.
The rationale, that the primary reason for deploying DSE
as part of an ANM scheme is to reduce instrumentation
costs and/or improve performance in the presence of
measurement errors or loss of communications, is one
that researchers continue to wrestle with. The cost and
performance implications for DSE have to be compared
with the cost and performance implications of additional
measurements.
CONCLUSIONS
This paper has discussed the requirements driving the
development of DSE on the Orkney Isles in Scotland.
Based on those requirements, the methods described in
this paper have been selected for trials which are due to
begin in the summer of 2013.
The error estimation technique has been highlighted as a
requirement of the DNO if DSE is to be successfully
applied. This paper has investigated the use of the
technique described in [2][3] to this end. The technique is
based on a number of assumptions, mainly that the
validity of the assumption that linearity can be assumed
across the ranges considered by τ and that no specific
treatment of parameter errors, i.e. error in the assumed
branch parameters, is considered. It is anticipated that the
forthcoming trials will provide data that will be used to
assess the impact of these assumptions and will be of
great interest to the wider power industry working on
these issues.
ACKNOWLEGDEMENTS
The authors would like to acknowledge the input of
David Wang and Weicong Cong into the early
exploration of the application of distribution state
estimation on the Orkney Isles.
REFERENCES
[1] The Orkney Smart Grid.
http://www.ssepd.co.uk/OrkneySmartGrid/
CIRED2013 Session 4
Paper No 1100
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